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arXiv · 0805.2558

Initial Value Problem of the Whitham Equations for the Camassa-Holm Equation

Tamara Grava·V. U. Pierce·Fei-Ran Tian
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Abstract

We study the Whitham equations for the Camassa-Holm equation. The equations are neither strictly hyperbolic nor genuinely nonlinear. We are interested in the initial value problem of the Whitham equations. When the initial values are given by a step function, the Whitham solution is self-similar. When the initial values are given by a smooth function, the Whitham solution exists within a cusp in the x-t plane. On the boundary of the cusp, the Whitham equation matches the Burgers solution, which exists outside the cusp.

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Tamara Grava, V. U. Pierce, Fei-Ran Tian. 2008-05-16. Initial Value Problem of the Whitham Equations for the Camassa-Holm Equation. https://doi.org/10.1016/j.physd.2008.08.016

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